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A Simple Tutorial on Exploratory Data Analysis¶

What is Exploratory Data Analysis (EDA)?¶

  • How to ensure you are ready to use machine learning algorithms in a project?
  • How to choose the most suitable algorithms for your data set?
  • How to define the feature variables that can potentially be used for machine learning?

Exploratory Data Analysis (EDA) helps to answer all these questions, ensuring the best outcomes for the project. It is an approach for summarizing, visualizing, and becoming intimately familiar with the important characteristics of a data set.

Value of Exploratory Data Analysis¶

Exploratory Data Analysis is valuable to data science projects since it allows to get closer to the certainty that the future results will be valid, correctly interpreted, and applicable to the desired business contexts. Such level of certainty can be achieved only after raw data is validated and checked for anomalies, ensuring that the data set was collected without errors. EDA also helps to find insights that were not evident or worth investigating to business stakeholders and data scientists but can be very informative about a particular business.

EDA is performed in order to define and refine the selection of feature variables that will be used for machine learning. Once data scientists become familiar with the data set, they often have to return to feature engineering step, since the initial features may turn out not to be serving their intended purpose. Once the EDA stage is complete, data scientists get a firm feature set they need for supervised and unsupervised machine learning.

Methods of Exploratory Data Analysis¶

It is always better to explore each data set using multiple exploratory techniques and compare the results. Once the data set is fully understood, it is quite possible that data scientist will have to go back to data collection and cleansing phases in order to transform the data set according to the desired business outcomes. The goal of this step is to become confident that the data set is ready to be used in a machine learning algorithm.

Exploratory Data Analysis is majorly performed using the following methods:

  • Univariate visualization — provides summary statistics for each field in the raw data set
  • Bivariate visualization — is performed to find the relationship between each variable in the dataset and the target variable of interest
  • Multivariate visualization — is performed to understand interactions between different fields in the dataset
  • Dimensionality reduction — helps to understand the fields in the data that account for the most variance between observations and allow for the processing of a reduced volume of data. Through these methods, the data scientist validates assumptions and identifies patterns that will allow for the understanding of the problem and model selection and validates that the data has been generated in the way it was expected to. So, value distribution of each field is checked, a number of missing values is defined, and the possible ways of replacing them are found.

Additional benefits Exploratory Data Analysis brings to projects Another side benefit of EDA is that it allows to specify or even define the questions you are trying to get the answer to from your data. Companies, that are only starting to leverage Data Science and AI technologies, often face the situation when they realize, that they have a lot of data and no ideas of what value that data can bring to their business decision making.

However, the questions always come first in data analysis. It doesn’t matter how much data company has, how many tools they have available, whether the data is historical or real time unless business stakeholders have the questions they are trying to solve with their data. EDA can help such companies to start formalizing the right questions, since with wrong questions you get the wrong answers, and take the wrong decisions.

Why skipping Exploratory Data Analysis is a bad idea?¶

In a hurry to get to the machine learning stage or simply impress business stakeholders very fast, data scientists tend to either entirely skip the exploratory process or do a very shallow work. It is a very serious and, sadly, common mistake of amateur data science consulting “professionals”.

Such inconsiderate behavior can lead to skewed data, with outliers and too many missing values and, therefore, some sad outcomes for the project:

  • generating inaccurate models;
  • generating accurate models on the wrong data;
  • choosing the wrong variables for the model;
  • inefficient use of the resources, including the rebuilding of the model.

Exploratory Data Analysis (EDA) is used on the one hand to answer questions, test business assumptions, generate hypotheses for further analysis. On the other hand, you can also use it to prepare the data for modeling.

The thing that these two probably have in common is a good knowledge of your data to either get the answers that you need or to develop an intuition for interpreting the results of future modeling.

There are a lot of ways to reach these goals as follows:

  1. Import the data

  2. Get a feel of the data ,describe the data,look at a sample of data like first and last rows

  3. Take a deeper look into the data by querying or indexing the data

  4. Identify features of interest

  5. Recognise the challenges posed by data - missing values, outliers

  6. Discover patterns in the data

One of the important things about EDA is Data profiling.

Data profiling is concerned with summarizing your dataset through descriptive statistics. You want to use a variety of measurements to better understand your dataset. The goal of data profiling is to have a solid understanding of your data so you can afterwards start querying and visualizing your data in various ways. However, this doesn’t mean that you don’t have to iterate: exactly because data profiling is concerned with summarizing your dataset, it is frequently used to assess the data quality. Depending on the result of the data profiling, you might decide to correct, discard or handle your data differently.

Key Concepts of Exploratory Data Analysis¶

  • 2 types of Data Analysis

    • Confirmatory Data Analysis

    • Exploratory Data Analysis

  • 4 Objectives of EDA

    • Discover Patterns

    • Spot Anomalies

    • Frame Hypothesis

    • Check Assumptions

  • 2 methods for exploration

    • Univariate Analysis

    • Bivariate Analysis

  • Stuff done during EDA

    • Trends

    • Distribution

    • Mean

    • Median

    • Outlier

    • Spread measurement (SD)

    • Correlations

    • Hypothesis testing

    • Visual Exploration

Overview¶

This is an exploratory data analysis on the House Prices Kaggle Competition found at

https://www.kaggle.com/c/house-prices-advanced-regression-techniques

Description¶

Ask a home buyer to describe their dream house, and they probably won't begin with the height of the basement ceiling or the proximity to an east-west railroad. But this playground competition's dataset proves that much more influences price negotiations than the number of bedrooms or a white-picket fence.

With 79 explanatory variables describing (almost) every aspect of residential homes in Ames, Iowa, this competition challenges you to predict the final price of each home.

There are 1460 instances of training data and 1460 of test data. Total number of attributes equals 81, of which 36 are numerical, 43 are categorical + Id and SalePrice.

Numerical Features: 1stFlrSF, 2ndFlrSF, 3SsnPorch, BedroomAbvGr, BsmtFinSF1, BsmtFinSF2, BsmtFullBath, BsmtHalfBath, BsmtUnfSF, EnclosedPorch, Fireplaces, FullBath, GarageArea, GarageCars, GarageYrBlt, GrLivArea, HalfBath, KitchenAbvGr, LotArea, LotFrontage, LowQualFinSF, MSSubClass, MasVnrArea, MiscVal, MoSold, OpenPorchSF, OverallCond, OverallQual, PoolArea, ScreenPorch, TotRmsAbvGrd, TotalBsmtSF, WoodDeckSF, YearBuilt, YearRemodAdd, YrSold

Categorical Features: Alley, BldgType, BsmtCond, BsmtExposure, BsmtFinType1, BsmtFinType2, BsmtQual, CentralAir, Condition1, Condition2, Electrical, ExterCond, ExterQual, Exterior1st, Exterior2nd, Fence, FireplaceQu, Foundation, Functional, GarageCond, GarageFinish, GarageQual, GarageType, Heating, HeatingQC, HouseStyle, KitchenQual, LandContour, LandSlope, LotConfig, LotShape, MSZoning, MasVnrType, MiscFeature, Neighborhood, PavedDrive, PoolQC, RoofMatl, RoofStyle, SaleCondition, SaleType, Street, Utilitif

Import Libraries¶

In [ ]:
import pandas as pd
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
import scipy.stats as st
from sklearn import ensemble, tree, linear_model
import missingno as msno

To start exploring your data, you’ll need to start by actually loading in your data. You’ll probably know this already, but thanks to the Pandas library, this becomes an easy task: you import the package as pd, following the convention, and you use the read_csv() function, to which you pass the URL in which the data can be found and a header argument. This last argument is one that you can use to make sure that your data is read in correctly: the first row of your data won’t be interpreted as the column names of your DataFrame.

Alternatively, there are also other arguments that you can specify to ensure that your data is read in correctly: you can specify the delimiter to use with the sep or delimiter arguments, the column names to use with names or the column to use as the row labels for the resulting DataFrame with index_col.

In [ ]:
train = pd.read_csv("train.csv")
test = pd.read_csv("test.csv")

One of the most elementary steps to do this is by getting a basic description of your data. A basic description of your data is indeed a very broad term: you can interpret it as a quick and dirty way to get some information on your data, as a way of getting some simple, easy-to-understand information on your data, to get a basic feel for your data. We can use the describe() function to get various summary statistics that exclude NaN values.

In [ ]:
train.describe()
Out[ ]:
Id MSSubClass LotFrontage LotArea OverallQual OverallCond YearBuilt YearRemodAdd MasVnrArea BsmtFinSF1 ... WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MoSold YrSold SalePrice
count 1460.000000 1460.000000 1201.000000 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000 1452.000000 1460.000000 ... 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000 1460.000000
mean 730.500000 56.897260 70.049958 10516.828082 6.099315 5.575342 1971.267808 1984.865753 103.685262 443.639726 ... 94.244521 46.660274 21.954110 3.409589 15.060959 2.758904 43.489041 6.321918 2007.815753 180921.195890
std 421.610009 42.300571 24.284752 9981.264932 1.382997 1.112799 30.202904 20.645407 181.066207 456.098091 ... 125.338794 66.256028 61.119149 29.317331 55.757415 40.177307 496.123024 2.703626 1.328095 79442.502883
min 1.000000 20.000000 21.000000 1300.000000 1.000000 1.000000 1872.000000 1950.000000 0.000000 0.000000 ... 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 2006.000000 34900.000000
25% 365.750000 20.000000 59.000000 7553.500000 5.000000 5.000000 1954.000000 1967.000000 0.000000 0.000000 ... 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 5.000000 2007.000000 129975.000000
50% 730.500000 50.000000 69.000000 9478.500000 6.000000 5.000000 1973.000000 1994.000000 0.000000 383.500000 ... 0.000000 25.000000 0.000000 0.000000 0.000000 0.000000 0.000000 6.000000 2008.000000 163000.000000
75% 1095.250000 70.000000 80.000000 11601.500000 7.000000 6.000000 2000.000000 2004.000000 166.000000 712.250000 ... 168.000000 68.000000 0.000000 0.000000 0.000000 0.000000 0.000000 8.000000 2009.000000 214000.000000
max 1460.000000 190.000000 313.000000 215245.000000 10.000000 9.000000 2010.000000 2010.000000 1600.000000 5644.000000 ... 857.000000 547.000000 552.000000 508.000000 480.000000 738.000000 15500.000000 12.000000 2010.000000 755000.000000

8 rows × 38 columns

Now that you have got a general idea about your data set, it’s also a good idea to take a closer look at the data itself. With the help of the head() and tail() functions of the Pandas library, you can easily check out the first and last lines of your DataFrame, respectively.

Let us look at some sample data

In [ ]:
train.head()
Out[ ]:
Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour Utilities ... PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold SaleType SaleCondition SalePrice
0 1 60 RL 65.0 8450 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 2 2008 WD Normal 208500
1 2 20 RL 80.0 9600 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 5 2007 WD Normal 181500
2 3 60 RL 68.0 11250 Pave NaN IR1 Lvl AllPub ... 0 NaN NaN NaN 0 9 2008 WD Normal 223500
3 4 70 RL 60.0 9550 Pave NaN IR1 Lvl AllPub ... 0 NaN NaN NaN 0 2 2006 WD Abnorml 140000
4 5 60 RL 84.0 14260 Pave NaN IR1 Lvl AllPub ... 0 NaN NaN NaN 0 12 2008 WD Normal 250000

5 rows × 81 columns

In [ ]:
train.tail()
Out[ ]:
Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour Utilities ... PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold SaleType SaleCondition SalePrice
1455 1456 60 RL 62.0 7917 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 8 2007 WD Normal 175000
1456 1457 20 RL 85.0 13175 Pave NaN Reg Lvl AllPub ... 0 NaN MnPrv NaN 0 2 2010 WD Normal 210000
1457 1458 70 RL 66.0 9042 Pave NaN Reg Lvl AllPub ... 0 NaN GdPrv Shed 2500 5 2010 WD Normal 266500
1458 1459 20 RL 68.0 9717 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 4 2010 WD Normal 142125
1459 1460 20 RL 75.0 9937 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 6 2008 WD Normal 147500

5 rows × 81 columns

In [ ]:
train.shape , test.shape
Out[ ]:
((1460, 81), (1459, 80))

Let us examine numerical features in the train dataset

In [ ]:
numeric_features = train.select_dtypes(include=[np.number])

numeric_features.columns
Out[ ]:
Index(['Id', 'MSSubClass', 'LotFrontage', 'LotArea', 'OverallQual',
       'OverallCond', 'YearBuilt', 'YearRemodAdd', 'MasVnrArea', 'BsmtFinSF1',
       'BsmtFinSF2', 'BsmtUnfSF', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF',
       'LowQualFinSF', 'GrLivArea', 'BsmtFullBath', 'BsmtHalfBath', 'FullBath',
       'HalfBath', 'BedroomAbvGr', 'KitchenAbvGr', 'TotRmsAbvGrd',
       'Fireplaces', 'GarageYrBlt', 'GarageCars', 'GarageArea', 'WoodDeckSF',
       'OpenPorchSF', 'EnclosedPorch', '3SsnPorch', 'ScreenPorch', 'PoolArea',
       'MiscVal', 'MoSold', 'YrSold', 'SalePrice'],
      dtype='object')

Let us examine categorical features in the train dataset

In [ ]:
categorical_features = train.select_dtypes(include=[object])
categorical_features.columns
Out[ ]:
Index(['MSZoning', 'Street', 'Alley', 'LotShape', 'LandContour', 'Utilities',
       'LotConfig', 'LandSlope', 'Neighborhood', 'Condition1', 'Condition2',
       'BldgType', 'HouseStyle', 'RoofStyle', 'RoofMatl', 'Exterior1st',
       'Exterior2nd', 'MasVnrType', 'ExterQual', 'ExterCond', 'Foundation',
       'BsmtQual', 'BsmtCond', 'BsmtExposure', 'BsmtFinType1', 'BsmtFinType2',
       'Heating', 'HeatingQC', 'CentralAir', 'Electrical', 'KitchenQual',
       'Functional', 'FireplaceQu', 'GarageType', 'GarageFinish', 'GarageQual',
       'GarageCond', 'PavedDrive', 'PoolQC', 'Fence', 'MiscFeature',
       'SaleType', 'SaleCondition'],
      dtype='object')

Visualising missing values for a sample of 250

In [ ]:
msno.matrix(train.sample(250))
Out[ ]:
<Axes: >
No description has been provided for this image

Heatmap¶

The missingno correlation heatmap measures nullity correlation: how strongly the presence or absence of one variable affects the presence of another:

In [ ]:
msno.heatmap(train)
Out[ ]:
<Axes: >
No description has been provided for this image
In [ ]:
msno.bar(train.sample(1000))
Out[ ]:
<Axes: >
No description has been provided for this image

Dendrogram¶

The dendrogram allows you to more fully correlate variable completion, revealing trends deeper than the pairwise ones visible in the correlation heatmap:

In [ ]:
msno.dendrogram(train)
Out[ ]:
<Axes: >
No description has been provided for this image

The dendrogram uses a hierarchical clustering algorithm (courtesy of scipy) to bin variables against one another by their nullity correlation (measured in terms of binary distance). At each step of the tree the variables are split up based on which combination minimizes the distance of the remaining clusters. The more monotone the set of variables, the closer their total distance is to zero, and the closer their average distance (the y-axis) is to zero.

To interpret this graph, read it from a top-down perspective. Cluster leaves which linked together at a distance of zero fully predict one another's presence—one variable might always be empty when another is filled, or they might always both be filled or both empty, and so on. In this specific example the dendrogram glues together the variables which are required and therefore present in every record.

Cluster leaves which split close to zero, but not at it, predict one another very well, but still imperfectly. If your own interpretation of the dataset is that these columns actually are or ought to be match each other in nullity , then the height of the cluster leaf tells you, in absolute terms, how often the records are "mismatched" or incorrectly filed—that is, how many values you would have to fill in or drop, if you are so inclined.

As with matrix, only up to 50 labeled columns will comfortably display in this configuration. However the dendrogram more elegantly handles extremely large datasets by simply flipping to a horizontal configuration.

The Challenges of Your Data

Now that we have gathered some basic information on your data, it’s a good idea to just go a little bit deeper into the challenges that the data might pose.

There are two factors mostly observed in EDA exercise which are missing values and outliers For understanding in detail on how to handle missing values in detail please visit https://www.kaggle.com/pavansanagapati/simple-tutorial-on-how-to-handle-missing-data For determining the outliers boxplot is used in the later part of this kernel

Estimate Skewness and Kurtosis

In [ ]:
numeric_features.skew(), numeric_features.kurt()
Out[ ]:
(Id                0.000000
 MSSubClass        1.407657
 LotFrontage       2.163569
 LotArea          12.207688
 OverallQual       0.216944
 OverallCond       0.693067
 YearBuilt        -0.613461
 YearRemodAdd     -0.503562
 MasVnrArea        2.669084
 BsmtFinSF1        1.685503
 BsmtFinSF2        4.255261
 BsmtUnfSF         0.920268
 TotalBsmtSF       1.524255
 1stFlrSF          1.376757
 2ndFlrSF          0.813030
 LowQualFinSF      9.011341
 GrLivArea         1.366560
 BsmtFullBath      0.596067
 BsmtHalfBath      4.103403
 FullBath          0.036562
 HalfBath          0.675897
 BedroomAbvGr      0.211790
 KitchenAbvGr      4.488397
 TotRmsAbvGrd      0.676341
 Fireplaces        0.649565
 GarageYrBlt      -0.649415
 GarageCars       -0.342549
 GarageArea        0.179981
 WoodDeckSF        1.541376
 OpenPorchSF       2.364342
 EnclosedPorch     3.089872
 3SsnPorch        10.304342
 ScreenPorch       4.122214
 PoolArea         14.828374
 MiscVal          24.476794
 MoSold            0.212053
 YrSold            0.096269
 SalePrice         1.882876
 dtype: float64,
 Id                -1.200000
 MSSubClass         1.580188
 LotFrontage       17.452867
 LotArea          203.243271
 OverallQual        0.096293
 OverallCond        1.106413
 YearBuilt         -0.439552
 YearRemodAdd      -1.272245
 MasVnrArea        10.082417
 BsmtFinSF1        11.118236
 BsmtFinSF2        20.113338
 BsmtUnfSF          0.474994
 TotalBsmtSF       13.250483
 1stFlrSF           5.745841
 2ndFlrSF          -0.553464
 LowQualFinSF      83.234817
 GrLivArea          4.895121
 BsmtFullBath      -0.839098
 BsmtHalfBath      16.396642
 FullBath          -0.857043
 HalfBath          -1.076927
 BedroomAbvGr       2.230875
 KitchenAbvGr      21.532404
 TotRmsAbvGrd       0.880762
 Fireplaces        -0.217237
 GarageYrBlt       -0.418341
 GarageCars         0.220998
 GarageArea         0.917067
 WoodDeckSF         2.992951
 OpenPorchSF        8.490336
 EnclosedPorch     10.430766
 3SsnPorch        123.662379
 ScreenPorch       18.439068
 PoolArea         223.268499
 MiscVal          701.003342
 MoSold            -0.404109
 YrSold            -1.190601
 SalePrice          6.536282
 dtype: float64)
In [ ]:
y = train['SalePrice']
plt.figure(1); plt.title('Johnson SU')
sns.distplot(y, kde=False, fit=st.johnsonsu)
plt.figure(2); plt.title('Normal')
sns.distplot(y, kde=False, fit=st.norm)
plt.figure(3); plt.title('Log Normal')
sns.distplot(y, kde=False, fit=st.lognorm)

/tmp/ipython-input-1021860808.py:3: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(y, kde=False, fit=st.johnsonsu)
/tmp/ipython-input-1021860808.py:5: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(y, kde=False, fit=st.norm)
/tmp/ipython-input-1021860808.py:7: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(y, kde=False, fit=st.lognorm)
Out[ ]:
<Axes: title={'center': 'Log Normal'}, xlabel='SalePrice'>
No description has been provided for this image
No description has been provided for this image
No description has been provided for this image

It is apparent that SalePrice doesn't follow normal distribution, so before performing regression it has to be transformed. While log transformation does pretty good job, best fit is unbounded Johnson distribution.

In [ ]:
sns.distplot(numeric_features.skew(),color='blue',axlabel ='Skewness')

/tmp/ipython-input-2476769313.py:1: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(numeric_features.skew(),color='blue',axlabel ='Skewness')
Out[ ]:
<Axes: xlabel='Skewness', ylabel='Density'>
No description has been provided for this image
In [ ]:
plt.figure(figsize = (12,8))
sns.distplot(train.kurt(),color='r',axlabel ='Kurtosis',norm_hist= False, kde = True,rug = False)
#plt.hist(train.kurt(),orientation = 'vertical',histtype = 'bar',label ='Kurtosis', color ='blue')
plt.show()
No description has been provided for this image
In [ ]:
plt.hist(train['SalePrice'],orientation = 'vertical',histtype = 'bar', color ='blue')
plt.show()
No description has been provided for this image
In [ ]:
target = np.log(train['SalePrice'])
target.skew()
plt.hist(target,color='blue')
Out[ ]:
(array([  5.,  12.,  54., 184., 470., 400., 220.,  90.,  19.,   6.]),
 array([10.46024211, 10.7676652 , 11.07508829, 11.38251138, 11.68993448,
        11.99735757, 12.30478066, 12.61220375, 12.91962684, 13.22704994,
        13.53447303]),
 <BarContainer object of 10 artists>)
No description has been provided for this image

Finding Correlation coefficients between numeric features and SalePrice

In [ ]:
correlation = numeric_features.corr()
print(correlation['SalePrice'].sort_values(ascending = False),'\n')

SalePrice        1.000000
OverallQual      0.790982
GrLivArea        0.708624
GarageCars       0.640409
GarageArea       0.623431
TotalBsmtSF      0.613581
1stFlrSF         0.605852
FullBath         0.560664
TotRmsAbvGrd     0.533723
YearBuilt        0.522897
YearRemodAdd     0.507101
GarageYrBlt      0.486362
MasVnrArea       0.477493
Fireplaces       0.466929
BsmtFinSF1       0.386420
LotFrontage      0.351799
WoodDeckSF       0.324413
2ndFlrSF         0.319334
OpenPorchSF      0.315856
HalfBath         0.284108
LotArea          0.263843
BsmtFullBath     0.227122
BsmtUnfSF        0.214479
BedroomAbvGr     0.168213
ScreenPorch      0.111447
PoolArea         0.092404
MoSold           0.046432
3SsnPorch        0.044584
BsmtFinSF2      -0.011378
BsmtHalfBath    -0.016844
MiscVal         -0.021190
Id              -0.021917
LowQualFinSF    -0.025606
YrSold          -0.028923
OverallCond     -0.077856
MSSubClass      -0.084284
EnclosedPorch   -0.128578
KitchenAbvGr    -0.135907
Name: SalePrice, dtype: float64

To explore further we will start with the following visualisation methods to analyze the data better:

  • Correlation Heat Map
  • Zoomed Heat Map
  • Pair Plot
  • Scatter Plot

Correlation Heat Map¶

In [ ]:
f , ax = plt.subplots(figsize = (14,12))

plt.title('Correlation of Numeric Features with Sale Price',y=1,size=16)

sns.heatmap(correlation,square = True,  vmax=0.8)
Out[ ]:
<Axes: title={'center': 'Correlation of Numeric Features with Sale Price'}>
No description has been provided for this image

The heatmap is the best way to get a quick overview of correlated features thanks to seaborn!

At initial glance it is observed that there are two red colored squares that get my attention.

  1. The first one refers to the 'TotalBsmtSF' and '1stFlrSF' variables.
  2. Second one refers to the 'GarageX' variables. Both cases show how significant the correlation is between these variables. Actually, this correlation is so strong that it can indicate a situation of multicollinearity. If we think about these variables, we can conclude that they give almost the same information so multicollinearity really occurs.

Heatmaps are great to detect this kind of multicollinearity situations and in problems related to feature selection like this project, it comes as an excellent exploratory tool.

Another aspect I observed here is the 'SalePrice' correlations.As it is observed that 'GrLivArea', 'TotalBsmtSF', and 'OverallQual' saying a big 'Hello !' to SalePrice, however we cannot exclude the fact that rest of the features have some level of correlation to the SalePrice. To observe this correlation closer let us see it in Zoomed Heat Map

Zoomed HeatMap¶

SalePrice Correlation matrix¶

In [ ]:
k= 11
cols = correlation.nlargest(k,'SalePrice')['SalePrice'].index
print(cols)
cm = np.corrcoef(train[cols].values.T)
f , ax = plt.subplots(figsize = (14,12))
sns.heatmap(cm, vmax=.8, linewidths=0.01,square=True,annot=True,cmap='viridis',
            linecolor="white",xticklabels = cols.values ,annot_kws = {'size':12},yticklabels = cols.values)

Index(['SalePrice', 'OverallQual', 'GrLivArea', 'GarageCars', 'GarageArea',
       'TotalBsmtSF', '1stFlrSF', 'FullBath', 'TotRmsAbvGrd', 'YearBuilt',
       'YearRemodAdd'],
      dtype='object')
Out[ ]:
<Axes: >
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From above zoomed heatmap it is observed that GarageCars & GarageArea are closely correlated . Similarly TotalBsmtSF and 1stFlrSF are also closely correlated.

My observations :

  • 'OverallQual', 'GrLivArea' and 'TotalBsmtSF' are strongly correlated with 'SalePrice'.
  • 'GarageCars' and 'GarageArea' are strongly correlated variables. It is because the number of cars that fit into the garage is a consequence of the garage area. 'GarageCars' and 'GarageArea' are like twin brothers. So it is hard to distinguish between the two. Therefore, we just need one of these variables in our analysis (we can keep 'GarageCars' since its correlation with 'SalePrice' is higher).
  • 'TotalBsmtSF' and '1stFloor' also seem to be twins. In this case let us keep 'TotalBsmtSF'
  • 'TotRmsAbvGrd' and 'GrLivArea', twins
  • 'YearBuilt' it appears like is slightly correlated with 'SalePrice'. This required more analysis to arrive at a conclusion may be do some time series analysis.

Pair Plot¶

Pair Plot between 'SalePrice' and correlated variables¶

Visualisation of 'OverallQual','TotalBsmtSF','GrLivArea','GarageArea','FullBath','YearBuilt','YearRemodAdd' features with respect to SalePrice in the form of pair plot & scatter pair plot for better understanding.

In [ ]:
sns.set()
columns = ['SalePrice','OverallQual','TotalBsmtSF','GrLivArea','GarageArea','FullBath','YearBuilt','YearRemodAdd']
sns.pairplot(train[columns],size = 2 ,kind ='scatter',diag_kind='kde')
plt.show()

/usr/local/lib/python3.12/dist-packages/seaborn/axisgrid.py:2100: UserWarning: The `size` parameter has been renamed to `height`; please update your code.
  warnings.warn(msg, UserWarning)
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Although we already know some of the main figures, this pair plot gives us a reasonable overview insight about the correlated features .Here are some of my analysis.

  • One interesting observation is between 'TotalBsmtSF' and 'GrLiveArea'. In this figure we can see the dots drawing a linear line, which almost acts like a border. It totally makes sense that the majority of the dots stay below that line. Basement areas can be equal to the above ground living area, but it is not expected a basement area bigger than the above ground living area.

  • One more interesting observation is between 'SalePrice' and 'YearBuilt'. In the bottom of the 'dots cloud', we see what almost appears to be a exponential function.We can also see this same tendency in the upper limit of the 'dots cloud'

  • Last observation is that prices are increasing faster now with respect to previous years.

Scatter Plot¶

Scatter plots between the most correlated variables¶

In [ ]:
fig, ((ax1, ax2), (ax3, ax4),(ax5,ax6)) = plt.subplots(nrows=3, ncols=2, figsize=(14,10))
OverallQual_scatter_plot = pd.concat([train['SalePrice'],train['OverallQual']],axis = 1)
sns.regplot(x='OverallQual',y = 'SalePrice',data = OverallQual_scatter_plot,scatter= True, fit_reg=True, ax=ax1)
TotalBsmtSF_scatter_plot = pd.concat([train['SalePrice'],train['TotalBsmtSF']],axis = 1)
sns.regplot(x='TotalBsmtSF',y = 'SalePrice',data = TotalBsmtSF_scatter_plot,scatter= True, fit_reg=True, ax=ax2)
GrLivArea_scatter_plot = pd.concat([train['SalePrice'],train['GrLivArea']],axis = 1)
sns.regplot(x='GrLivArea',y = 'SalePrice',data = GrLivArea_scatter_plot,scatter= True, fit_reg=True, ax=ax3)
GarageArea_scatter_plot = pd.concat([train['SalePrice'],train['GarageArea']],axis = 1)
sns.regplot(x='GarageArea',y = 'SalePrice',data = GarageArea_scatter_plot,scatter= True, fit_reg=True, ax=ax4)
FullBath_scatter_plot = pd.concat([train['SalePrice'],train['FullBath']],axis = 1)
sns.regplot(x='FullBath',y = 'SalePrice',data = FullBath_scatter_plot,scatter= True, fit_reg=True, ax=ax5)
YearBuilt_scatter_plot = pd.concat([train['SalePrice'],train['YearBuilt']],axis = 1)
sns.regplot(x='YearBuilt',y = 'SalePrice',data = YearBuilt_scatter_plot,scatter= True, fit_reg=True, ax=ax6)
YearRemodAdd_scatter_plot = pd.concat([train['SalePrice'],train['YearRemodAdd']],axis = 1)
YearRemodAdd_scatter_plot.plot.scatter('YearRemodAdd','SalePrice')
Out[ ]:
<Axes: xlabel='YearRemodAdd', ylabel='SalePrice'>
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In [ ]:
saleprice_overall_quality= train.pivot_table(index ='OverallQual',values = 'SalePrice', aggfunc = np.median)
saleprice_overall_quality.plot(kind = 'bar',color = 'blue')
plt.xlabel('Overall Quality')
plt.ylabel('Median Sale Price')
plt.show()

/tmp/ipython-input-4265127396.py:1: FutureWarning: The provided callable <function median at 0x7f5a23690d60> is currently using DataFrameGroupBy.median. In a future version of pandas, the provided callable will be used directly. To keep current behavior pass the string "median" instead.
  saleprice_overall_quality= train.pivot_table(index ='OverallQual',values = 'SalePrice', aggfunc = np.median)
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Box plot - OverallQual¶

In [ ]:
var = 'OverallQual'
data = pd.concat([train['SalePrice'], train[var]], axis=1)
f, ax = plt.subplots(figsize=(12, 8))
fig = sns.boxplot(x=var, y="SalePrice", data=data)
fig.axis(ymin=0, ymax=800000);
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Box plot - Neighborhood¶

In [ ]:
var = 'Neighborhood'
data = pd.concat([train['SalePrice'], train[var]], axis=1)
f, ax = plt.subplots(figsize=(16, 10))
fig = sns.boxplot(x=var, y="SalePrice", data=data)
fig.axis(ymin=0, ymax=800000);
xt = plt.xticks(rotation=45)
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Count Plot - Neighborhood¶

In [ ]:
plt.figure(figsize = (12, 6))
sns.countplot(x = 'Neighborhood', data = data)
xt = plt.xticks(rotation=45)
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Based on the above observation can group those Neighborhoods with similar housing price into a same bucket for dimension-reduction.Let us see this in the preprocessing stage

With qualitative variables we can check distribution of SalePrice with respect to variable values and enumerate them.

In [ ]:
for c in categorical_features:
    train[c] = train[c].astype('category')
    if train[c].isnull().any():
        train[c] = train[c].cat.add_categories(['MISSING'])
        train[c] = train[c].fillna('MISSING')

def boxplot(x, y, **kwargs):
    sns.boxplot(x=x, y=y)
    x=plt.xticks(rotation=90)
f = pd.melt(train, id_vars=['SalePrice'], value_vars=categorical_features)
g = sns.FacetGrid(f, col="variable",  col_wrap=2, sharex=False, sharey=False, size=5)
g = g.map(boxplot, "value", "SalePrice")
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Housing Price vs Sales¶

  • Sale Type & Condition
  • Sales Seasonality
In [ ]:
var = 'SaleType'
data = pd.concat([train['SalePrice'], train[var]], axis=1)
f, ax = plt.subplots(figsize=(16, 10))
fig = sns.boxplot(x=var, y="SalePrice", data=data)
fig.axis(ymin=0, ymax=800000);
xt = plt.xticks(rotation=45)
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In [ ]:
var = 'SaleCondition'

data = pd.concat([train['SalePrice'], train[var]], axis=1)

f, ax = plt.subplots(figsize=(16, 10))

fig = sns.boxplot(x=var, y="SalePrice", data=data)

fig.axis(ymin=0, ymax=800000);

xt = plt.xticks(rotation=45)
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ViolinPlot - Functional vs.SalePrice¶

In [ ]:
sns.violinplot(x='Functional', y='SalePrice', data = train)
Out[ ]:
<Axes: xlabel='Functional', ylabel='SalePrice'>
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FactorPlot - FirePlaceQC vs. SalePrice¶

In [ ]:
sns.catplot(x='FireplaceQu', y='SalePrice', data = train, color = 'm', \
               estimator = np.median, order = ['Ex', 'Gd', 'TA', 'Fa', 'Po'], height = 4.5,  aspect=1.35)
Out[ ]:
<seaborn.axisgrid.FacetGrid at 0x7f59e09d3ef0>
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Facet Grid Plot - FirePlace QC vs.SalePrice¶

In [ ]:
g = sns.FacetGrid(train, col = 'FireplaceQu', col_wrap = 3, col_order=['Ex', 'Gd', 'TA', 'Fa', 'Po'])
g.map(sns.boxplot, 'Fireplaces', 'SalePrice', order = [1, 2, 3], palette = 'Set2')

/usr/local/lib/python3.12/dist-packages/seaborn/axisgrid.py:854: FutureWarning: 

Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.

  func(*plot_args, **plot_kwargs)
/usr/local/lib/python3.12/dist-packages/seaborn/axisgrid.py:854: FutureWarning: 

Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.

  func(*plot_args, **plot_kwargs)
/usr/local/lib/python3.12/dist-packages/seaborn/axisgrid.py:854: FutureWarning: 

Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.

  func(*plot_args, **plot_kwargs)
/usr/local/lib/python3.12/dist-packages/seaborn/axisgrid.py:854: FutureWarning: 

Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.

  func(*plot_args, **plot_kwargs)
/usr/local/lib/python3.12/dist-packages/seaborn/axisgrid.py:854: FutureWarning: 

Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.

  func(*plot_args, **plot_kwargs)
Out[ ]:
<seaborn.axisgrid.FacetGrid at 0x7f59da11d730>
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PointPlot¶

In [ ]:
plt.figure(figsize=(8,10))
g1 = sns.pointplot(x='Neighborhood', y='SalePrice',
                   data=train, hue='LotShape')
g1.set_xticklabels(g1.get_xticklabels(),rotation=90)
g1.set_title("Lotshape Based on Neighborhood", fontsize=15)
g1.set_xlabel("Neighborhood")
g1.set_ylabel("Sale Price", fontsize=12)
plt.show()

/tmp/ipython-input-345703946.py:4: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
  g1.set_xticklabels(g1.get_xticklabels(),rotation=90)
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Missing Value Analysis¶

Numeric Features¶

In [ ]:
total = numeric_features.isnull().sum().sort_values(ascending=False)
percent = (numeric_features.isnull().sum()/numeric_features.isnull().count()).sort_values(ascending=False)
missing_data = pd.concat([total, percent], axis=1,join='outer', keys=['Total Missing Count', '% of Total Observations'])
missing_data.index.name =' Numeric Feature'

missing_data.head(20)
Out[ ]:
Total Missing Count % of Total Observations
Numeric Feature
LotFrontage 259 0.177397
GarageYrBlt 81 0.055479
MasVnrArea 8 0.005479
LotArea 0 0.000000
MSSubClass 0 0.000000
Id 0 0.000000
OverallCond 0 0.000000
OverallQual 0 0.000000
YearRemodAdd 0 0.000000
YearBuilt 0 0.000000
BsmtFinSF2 0 0.000000
BsmtUnfSF 0 0.000000
TotalBsmtSF 0 0.000000
BsmtFinSF1 0 0.000000
2ndFlrSF 0 0.000000
LowQualFinSF 0 0.000000
GrLivArea 0 0.000000
BsmtFullBath 0 0.000000
BsmtHalfBath 0 0.000000
FullBath 0 0.000000

Missing values for all numeric features in Bar chart Representation¶

In [ ]:
missing_values = numeric_features.isnull().sum(axis=0).reset_index()
missing_values.columns = ['column_name', 'missing_count']
missing_values = missing_values.loc[missing_values['missing_count']>0]
missing_values = missing_values.sort_values(by='missing_count')

ind = np.arange(missing_values.shape[0])
width = 0.1
fig, ax = plt.subplots(figsize=(12,3))
rects = ax.barh(ind, missing_values.missing_count.values, color='b')
ax.set_yticks(ind)
ax.set_yticklabels(missing_values.column_name.values, rotation='horizontal')
ax.set_xlabel("Missing Observations Count")
ax.set_title("Missing Observations Count - Numeric Features")
plt.show()
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Categorical Features¶

In [ ]:
total = categorical_features.isnull().sum().sort_values(ascending=False)
percent = (categorical_features.isnull().sum()/categorical_features.isnull().count()).sort_values(ascending=False)
missing_data = pd.concat([total, percent], axis=1,join='outer', keys=['Total Missing Count', ' % of Total Observations'])
missing_data.index.name ='Feature'
missing_data.head(20)
Out[ ]:
Total Missing Count % of Total Observations
Feature
PoolQC 1453 0.995205
MiscFeature 1406 0.963014
Alley 1369 0.937671
Fence 1179 0.807534
MasVnrType 872 0.597260
FireplaceQu 690 0.472603
GarageFinish 81 0.055479
GarageQual 81 0.055479
GarageType 81 0.055479
GarageCond 81 0.055479
BsmtFinType2 38 0.026027
BsmtExposure 38 0.026027
BsmtFinType1 37 0.025342
BsmtQual 37 0.025342
BsmtCond 37 0.025342
Electrical 1 0.000685
Condition1 0 0.000000
Condition2 0 0.000000
LotShape 0 0.000000
Street 0 0.000000

Missing values for Categorical features in Bar chart Representation¶

In [ ]:
missing_values = categorical_features.isnull().sum(axis=0).reset_index()
missing_values.columns = ['column_name', 'missing_count']
missing_values = missing_values.loc[missing_values['missing_count']>0]
missing_values = missing_values.sort_values(by='missing_count')

ind = np.arange(missing_values.shape[0])
width = 0.9
fig, ax = plt.subplots(figsize=(12,18))
rects = ax.barh(ind, missing_values.missing_count.values, color='red')
ax.set_yticks(ind)
ax.set_yticklabels(missing_values.column_name.values, rotation='horizontal')
ax.set_xlabel("Missing Observations Count")
ax.set_title("Missing Observations Count - Categorical Features")
plt.show()
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Categorical Feature Exploration¶

In [ ]:
for column_name in train.columns:
    if train[column_name].dtypes == 'object':
        train[column_name] = train[column_name].fillna(train[column_name].mode().iloc[0])
        unique_category = len(train[column_name].unique())
        print("Feature '{column_name}' has '{unique_category}' unique categories".format(column_name = column_name,
                                                                                         unique_category=unique_category))

for column_name in test.columns:
    if test[column_name].dtypes == 'object':
        test[column_name] = test[column_name].fillna(test[column_name].mode().iloc[0])
        unique_category = len(test[column_name].unique())
        print("Features in test set '{column_name}' has '{unique_category}' unique categories".format(column_name = column_name, unique_category=unique_category))

Features in test set 'MSZoning' has '5' unique categories
Features in test set 'Street' has '2' unique categories
Features in test set 'Alley' has '2' unique categories
Features in test set 'LotShape' has '4' unique categories
Features in test set 'LandContour' has '4' unique categories
Features in test set 'Utilities' has '1' unique categories
Features in test set 'LotConfig' has '5' unique categories
Features in test set 'LandSlope' has '3' unique categories
Features in test set 'Neighborhood' has '25' unique categories
Features in test set 'Condition1' has '9' unique categories
Features in test set 'Condition2' has '5' unique categories
Features in test set 'BldgType' has '5' unique categories
Features in test set 'HouseStyle' has '7' unique categories
Features in test set 'RoofStyle' has '6' unique categories
Features in test set 'RoofMatl' has '4' unique categories
Features in test set 'Exterior1st' has '13' unique categories
Features in test set 'Exterior2nd' has '15' unique categories
Features in test set 'MasVnrType' has '3' unique categories
Features in test set 'ExterQual' has '4' unique categories
Features in test set 'ExterCond' has '5' unique categories
Features in test set 'Foundation' has '6' unique categories
Features in test set 'BsmtQual' has '4' unique categories
Features in test set 'BsmtCond' has '4' unique categories
Features in test set 'BsmtExposure' has '4' unique categories
Features in test set 'BsmtFinType1' has '6' unique categories
Features in test set 'BsmtFinType2' has '6' unique categories
Features in test set 'Heating' has '4' unique categories
Features in test set 'HeatingQC' has '5' unique categories
Features in test set 'CentralAir' has '2' unique categories
Features in test set 'Electrical' has '4' unique categories
Features in test set 'KitchenQual' has '4' unique categories
Features in test set 'Functional' has '7' unique categories
Features in test set 'FireplaceQu' has '5' unique categories
Features in test set 'GarageType' has '6' unique categories
Features in test set 'GarageFinish' has '3' unique categories
Features in test set 'GarageQual' has '4' unique categories
Features in test set 'GarageCond' has '5' unique categories
Features in test set 'PavedDrive' has '3' unique categories
Features in test set 'PoolQC' has '2' unique categories
Features in test set 'Fence' has '4' unique categories
Features in test set 'MiscFeature' has '3' unique categories
Features in test set 'SaleType' has '9' unique categories
Features in test set 'SaleCondition' has '6' unique categories